相关论文: Analytic trajectory bootstrap for matrix models

We bootstrap the $4$-point amplitude of $\mathcal{N}=2$ hypermultiplets in $\text{AdS}_2 \times \text{S}^2$ at tree-level and for arbitrary external weights. We hereby explicitly demonstrate the existence of a hidden four-dimensional…

Large language models struggle to maintain strict adherence to structured workflows in high-stakes domains such as healthcare triage. Monolithic approaches that encode entire decision structures within a single prompt are prone to…

Current frontier large-language models rely on reasoning to achieve state-of-the-art performance. Many existing interpretability are limited in this area, as standard methods have been designed to study single forward passes of a model…

Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of…

In this paper we present a new algorithm for computing a low rank approximation of the product $A^TB$ by taking only a single pass of the two matrices $A$ and $B$. The straightforward way to do this is to (a) first sketch $A$ and $B$…

An increasing amount of trajectory data is being annotated with text descriptions to better capture the semantics associated with locations. The fusion of spatial locations and text descriptions in trajectories engenders a new type of…

As Large Language Models (LLMs) evolve into persistent scientific collaborators, context window saturation has emerged as a critical bottleneck. Scientific workflows involving iterative data analysis and hypothesis refinement rapidly…

Self-supervised word embedding algorithms such as word2vec provide a minimal setting for studying representation learning in language modeling. We examine the quartic Taylor approximation of the word2vec loss around the origin, and we show…

Large language models (LLMs) can achieve highly effective performance on various reasoning tasks by incorporating step-by-step chain-of-thought (CoT) prompting as demonstrations. However, the reasoning chains of demonstrations generated by…

This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next'). Each atomic proposition is assumed to represent a state space region described by a…

We give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM…

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS…

The spectra of recently constructed auxiliary matrices for the six-vertex model respectively the spin s=1/2 Heisenberg chain at roots of unity q^N=1 are investigated. Two conjectures are formulated both of which are proven for N=3 and are…

Pretrained speech representations like wav2vec2 and HuBERT exhibit strong anisotropy, leading to high similarity between random embeddings. While widely observed, the impact of this property on downstream tasks remains unclear. This work…

The study of finite J effects for the light-cone AdS superstring by means of the Thermodynamic Bethe Ansatz requires an understanding of a companion 2d theory which we call the mirror model. It is obtained from the original string model by…

We study families of one-dimensional CFTs relevant for describing gapped QFTs in AdS$_2$. Using the Polyakov bootstrap as our main tool, we explain how S-matrices emerge from the flat space limit of CFT correlators. In this limit we prove…

This work gives an overview of analytic tools for the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools…

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and…

The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This…